Percolation:

• Sites of a lattice occupied with probability p
• "Clusters"; groups of neighboring occupied sites
• Percolation; for p > p_c, a cluster extends across entire lattice

p = 0.2, 0.4, 0.6, 0.8;

Fire or epedemic;

• Initial fire/outbreak
• Nearest neighbor interaction

p = 0.46 - 0.48;

A more elaborate model

• Landscape variations, wind
• Modify interactions (eg., require two burning neighbors)
• Mixtures of types of trees (fuel)
• 'Crawling' and 'crown' fires
• Jumping fires

Some goals

• Average behavior over many instances at same p
• Behavior above and below p_c
• Lifetime of forest fire
• Diagnostics for evaluating risk
• Strategies for fighting fires
• Suggestions for prevention

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Resources

• MATLAB program
• Forest Fire entry in Wikipedia
• Forest Fires webpage of Natural Resources Canada (NRC)
• Fire growth models at the NRC website
• Percolation: Fractals and Fires in Random Forests in Chaos and Fractals: New Frontiers of Science, H-O Peitgen, H Jurgens, D Saupe. Springer, 2004.
• Introduction to Percolation Theory, D Stauffer, A Aharony. Taylor and Francis, 1992.
• Fractals and Disordered Systems, A Bunde, S Havlin (editors). Springer, 1996.